Clayton Donaldson's first Brentford goal proved to be the winner as The Bees picked up their first League One away win of the season.
Jonathan Douglas will almost certainly be claiming the opening goal that has been given as a James Dunne own goal and Donaldson doubled the lead before half time.
Exeter pulled one back in the second half and dominated territory for long stages but with Leon Legge and Karleigh Osborne outstanding, Brentford did enough to take the points and a win they dedicated to the memory of former Kit Man Dave Carter, who lost a battle with cancer less than 24 hours before kick off.
Chris Shephard shot wide for the hosts inside the first 45 seconds and they will probably feel they had the better of the first 20 minutes, albeit they found themselves a goal down.
Sam Saunders shot wide early on for The Bees but there were few chances of note before Brentford took the lead.
Saunders bought his team ten yards after a quick free kick and when Douglas lined up the second effort it took a wicked deflection off Dunne and beat Artur Krysiak all ends up.
Nicholas Bignall had lifted an effort over for the home side after a collision between Osborne and Craig Woodman before the goal and they had much the better of things immediately after the opener.
A Liam Sercombe shot deflected narrowly wide off Douglas and David Noble chipped an effort over the bar.
Richard Lee held on well to another Noble effort and the Exeter midfield man fired over soon after.
Legge blocked superbly from a Sercombe effort and Osborne produced an even better one to deny Dunne before Troy Archibald-Henville flicked a header just wide.
Exeter had unquestionably dominated territory and possession but Brentford gave them a lesson in how to use the ball eight minutes before the break.
Woodman chipped a ball down the left flank for Niall McGinn to run on to, the Northern Ireland international teased Steve Tully before crossing for Donaldson to power a header home from close range.
Lee held on to a Bignall header but Brentford's second goal knocked the stuffing out of Exeter.
The introduction of Guillem Bauza gave them a new lease of life and the striker almost scored within 45 seconds of the re-start when his shot from a Shephard cut back deflected inches wide.
Bignall headed wide soon after and substitute Tom Nichols rolled an effort wide after beating Lee to the ball but Brentford started to regain a measure of control.
Archibald-Henville made an important tackle to prevent Donaldson finishing off a four man move and the striker headed wide when unmarked from the resulting corner.
Donaldson shot over after picking up an Alexander lay off but Exeter soon had the upper hand again, helped by going a little more direct.
Lee saved from Shephard and then did well to palm an Archibald-Henville header over the top.
The goal Exeter had been threatening all night came midway through the half.
Nichols barged his way past Legge and went down when the Brentford defender returned the favour.
Assistant referee Chris Powell signalled for a penalty and Bauza stroked it high to Lee's left to halve the arrears.
Krysiak saved at the feet of Donaldson as Brentford tried to strike straight back while Dunne and Shephard both lashed over at the other end.
Saunders brought a save out of Krysiak with a curling free kick and McGinn volleyed wide while Shephard fired a shot inches wide at the other end.
As time ticked by, Exeter started to throw more and more men forward - Archibald-Henville headed wide from close range but Brentford held firm to pick up the points
Exeter City: Krysiak; Tully, Archibald-Henville, Duffy, Golbourne; Dunne, Noble, Sercombe (sub Jones 88 mins); Shephard; Bignall (sub Nichols 54 mins), Logan (sub Bauza h/t)
Subs (not used): Pidgely, Coles
Bookings: Noble (7 mins)
Brentford: Lee; Logan, Legge, Osborne, Woodman; Saunders (sub Weston 76 mins), Douglas, Reeves (sub O'Connor 61 mins), McGinn (sub Forrester 90 mins); Alexander, Donaldson
Subs (not used): Moore, Eger
Bookings: Alexander (31 mins), Saunders (66 mins), Woodman (81 mins), Weston (85 mins)
Attendance: 4,344 (344 Bees fans)
By Chris Wickham